A243859 Primes p for which p^i + 4 is prime for i = 1, 3, 5 and 7.

7, 133153, 184039, 356929, 469363, 982843, 2154487, 2552713, 2686573, 3378103, 3847867, 4270069, 4341373, 4564363, 4584847, 4964899, 5366017, 5600989, 6185173, 6592609, 6595597, 6629683, 6768409, 8232277, 9028429, 9964177, 10009339, 12107089, 13266553, 13600189

Offset: 1

Author

Abhiram R Devesh, Jun 12 2014

Keywords

• nonn

Comments

This is a subsequence of A243780: Primes p for which p^i + 4 is prime for i = 1, 3 and 5.

Examples

			p=7 is in this sequence as p + 4 = 11 (prime), p^3 + 4 = 347 (prime), p^5 + 4 = 16811 (prime), and p^7 + 4 = 823547 (prime).
		

Links

• Abhiram R Devesh, Table of n, a(n) for n = 1..141

Crossrefs

Cf. A023200, A243583, A243780.

Programs

Maple

p := 2:
for  n from 1 do
    if isprime(p+4) and isprime(p^3+4) and isprime(p^5+4) and isprime(p^7+4) then
        print(p) ;
    end if;
    p := nextprime(p) ;
end do: # R. J. Mathar, Jun 13 2014

Mathematica

Select[Prime[Range[900000]],AllTrue[#^{1,3,5,7}+4,PrimeQ]&] (* Harvey P. Dale, Apr 12 2022 *)

Python

import sympy.ntheory as snt
n=2
while n>1:
    n1=n+4
    n2=((n**3)+4)
    n3=((n**5)+4)
    n4=((n**7)+4)
    ##Check if n1 , n2, n3 and n4 are also primes.
    if snt.isprime(n1)== True and snt.isprime(n2)== True and snt.isprime(n3)== True and snt.isprime(n4)== True:
        print(n, n1, n2, n3, n4)
    n=snt.nextprime(n)